1.Algebra Booster

5.10 Algebra Booster
(i) at least one cube is white?
(ii) at least one cube is red?
171. There are n students in a class and a group of three is
taken by class teacher to zoo. The same set of three
children is not taken more than once. It is found that he
goes to zoo 84 times more than the visits of a particular
child, find the value of n.
172. In a club election, the number of contestants is one
more than the maximum number of the candidates
which a voter can vote for. If the total number of ways
a voter can vote is 126, find the number of contestants.
173. In a chess tournament, the participants were to play
one game with one another. Two players fell ill having
played 6 games each and without playing with each
other. If the total number of games played is 117, find
the number of participants at the beginning.
174. A person is permitted to select at least 1 and atmost n
coins from a collection of (2n +1) distinct coins. If the
total number of ways in which it can be done is 255,
find the value of n.
175. A student is allowed to select atmost n books from a
(2n +1) books. If the total number ways he can select
at least one book is 63, find the value of n.
COMBINATIONS FROM IDENTICAL OBJECTS
176. In how many ways, Master Hemant can select 10 red
balls out of 20 red balls?
177. In how many ways, Master Kalicharan can select zero
or more balls from 12 green balls?
178. In how many ways, Master Bheem can select at least 1
ball out of 10 red balls, 15 green balls, 12 blue balls and
5 black balls?
179. Out of 6 apples, 5 mangoes and 4 bananas, how many
selections of fruits can be made?
180. Out of 6 apples, 5 mangoes and 7 bananas, how many
selections of fruits can be made such that at least one
fruit of each type is always included?
181. Out of 10 apples, 6 mangoes and 4 bananas, how many
selections of fruits can be made such that at least one
mongo is always included?
182. In a fruit basket, 4 mangoes, 5 bananas and 3 different
types of fruits are kept. In how many ways one can
select fruits from this fruit basket?
183. Find the number of ways in which one or more letters be
selected from the letter of the word ABRACADABRA.
184. Find the number of ways in which one or more letters
be selected from the letter of the word MATHEMAT-
ICS.
185. Find the number of ways in which one or more letters
be selected from the letters of the sequence DADDY
DID A DEADLY DEED.
186. Find the number of ways in which a selection of 4 letters
can be made from the letters of the word PROPOR-
TION.
187. Find the number of ways in which an arrangement of 4
letters can be made from the letters of the word PRO-
PORTION.
188. Find the number of ways in which a selection of 4 letters
can be made from the letters of the word MATH-
EMATICS.
189. Find the number of ways in which an arrangement of 4
letters can be made from the letters of the word MATH-
EMATICS.
190. Find the number of ways in which a selection of 4 letters
can be made from the letters of the word PASS-
PORT.
191. Find the number of ways in which an arrangement of 4
letters can be made from the letters of the word PASS-
PORT.
192. Find the number of ways in which we can select 5 letters
of the word INTERNATIONAL.
193. Find the number of ways in which an arrangement of
5 letters can be made from the letters of the word IN-
TERNATIONAL.
DIVISOR OF A GIVEN NATURAL NUMBER
194. If a = 10800, find the
(i) total number of divisors of a
(ii) the number of even divisors of a
(iii) the number of divisors a of the form (4m + 2)
(iv) the number of divisors a, which are multiple of 15.
195. In how many ways, the number 18900 can be split into
two factors which are relatively prime or co-prime?
196. Find the number of ordered pairs (p, q) such that LCM
of p and q is 2520.
197. Find the sum of all divisors of 2520.
198. Find the sum of all odd divisors of 360.
199. Find the sum of all even divisors of 38808.
200. Find the sum of all factors of 7200 that ends with 5.
201. How many number less than 10000 has only 3 factors?
202. In how many ways 8100 can be resolved into product
of two factors?
203. In how many ways 10800 can be resolved as a product
of two factors?
DISTRIBUTION INTO GROUPS
204. In how many ways 4 different things can be divided
P, Q, R and S into 2 sets one having 1 thing and second
set having 3 things respectively?
205. In how many ways 4 different things can be distributed
among 2 persons such that one having 3 things and
other gets 1 thing respectively?
206. In how many ways 4 different things can be divided
P, Q, R and S into 2 sets such that each having 2 things
respectively?
207. In how many ways 4 different things can be distributed
between 2 persons such that each gets 2 things respectively?